The phrase suggests it's smart to evade risky situations rather than face them head-on. When Jim saw the angry dogs, he decided that discretion is the better part of valour and walked away.
Pro Tip 2/3
Subtle Wisdom
Using the phrase implies a subtle intelligence in choosing safety over heroism. In the heated argument, Laura chose to remain silent, knowing discretion is the better part of valour.
Pro Tip 3/3
Historical Roots
Understand it's an old idiom, originating from Shakespeare's works, giving it a literary flair. Reading Shakespeare, one realizes where 'discretion is the better part of valour' comes from.